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1、07线性代数讲义1 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 5 D Z=:x|x . N0=:x|xZ,x0.N=:x|xZ,x0.Q=:x|xkn.R=:x|x.C=:x|xE.Pvkn ! !E 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 1 1.1 n01 1 (1).10I | (a)|=a a 11a12 (2).20I =a11a22 a12a21 a21a22 12 X =4 6= 2 34 a11a12a13 (3).30I a21a22a23 a31a32a33 =a11 a22a33+a
2、12 a23a31+a21a32a13 a31a22a13 a21a12a33 a12a23a31 2 12 X 110 =2 312 123 246 =0 312 (4)p0I ds 5Vg: 1.1d1,2,n| kS|.i1,i2,in n? , 1,2,n n?IO . X:1,2,3,4 2,1,4,3 2,3,1,44? . 1.2 i1,i2,in n? ,Xtss isis ,ois is _S. _So, _S.P (i1,i2,in) y = _ _ 12345 0 : 13245(32)1 (42),(43)2 14235 14352(43),(42),(52),(32)
3、4 1.3Xt_S,o ;Xt_S,o . n1.4n? v g _SUC5. y.#i1,i2,inn? ,is is+m j1,j2,jn yy(i1,i2,in) (j1,j2,jn)Sm=1 w,. 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 (i1,i2,is,is+1,is+k,is+k+1,in)vmg x(i1,i2,is+m,is,is+1,is+m 1,is+m+Pvm 1g x1uj1,j2,jn.d(i1,i2,in)SUg 2m 1g,(j1,j2,jn)Ug (i1,i2,in)S. n1.5(1).Xt j1,j2,jnd
4、g, vtg ,o(j1,j2,jn) t. (2).Xt i1,i2,invtg g, ,o(i1,i2,in) t. vtg y.(1).j1,j2,jn1,2,n,oj1,j2,jnSUg tg.Xt(j1,j2,jn),1,2,n ,dt . ,Xt(j1,j2,jn) ,ot ,d(j1,j2,jn) tS. (2).aqy.2 n1.6Xt j1,j2,jnn? , ji1=1,ji2=2,jin=n,o(j1,j2,jn) (i1,i2,in). j1j2jn12nvtg y.dn1.5 12nj1j2jn vtg vtg Xtj1,j2,jn1,2,n,o1,2,ni1,i2,
5、in.dn1.5 ,(j1,j2,jn) (i1,i2,in).2 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 1.2 ,123 k 123 (),132(),213(),231(),312(),321 a11a12a13 (),d a21a22a23 =( 1)(i1i2i3)a1i1a2i2a3i3. a31a32a33 a1100 a 21a220 .O :(1).D= =a11ann. a n1an2ann 00a1n 0an(n 1)0 2(n 1) (2).D= =( 1)an1a1n. a00 n1 :P56,1.21.I O e I .
6、 0b1000 000a1 00b002 a000 2 (1). =a1a2a3 an.(2). 000b30 =a1b1b2b3b4. 0a300 0000b 4 00a 0n a1a2a3a4a5 a 11a12a13a14a15 a21a22a23a24a25 (3). a31a32000 =0. 00 a41a420 a51a52000 2.!40I k K kfa11a23 . 3.y:eQ n0I 1u0 un2 n,uTI 0. 4.ytij,(1)1274i56j9 ,(2)1i25j4897 .1.3 1 5 =( 1)(i1,i2,in)a1i1anin(I a 11a12
7、 ).kw ,n0I : =( 1)(i1i2)a1i1a2i2. a21a22 n01 a11a12a1n a 21a22a2n D= a n1an2ann zI O , A S .XtI DI p , I = 5I ,P D . 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 2 12 213 X 110 = 111 312 202 5 1.7D=D. a11a 12a 1n a11a12a1n a 21a22a2n a21a22a2n y.PD= . ,D= a an1an2ann n1an2ann (i1,i2,in) D=( 1)a1i1anin
8、,D=( 1)(j1,j2,jn)a1j1anjn.d= aij=aji.? j1,j2,jn,-i1,i2,in,ji1=1,ji2=2,jin=n.w( 1)(j1,j2,jn)a1j1anjn =( 1)(j1,j2,jn)aj11ajnn=( 1)(j1,j2,jn)a1i1anin=( 1)(i1,i2,in)a1i1anin D=D. 5 1.8 1 1, #1 UC. at1at2atn as1as2asn y.#I D= ,D1= . as1as2asn at1at2atn yD= D1.dI D1=( 1)(i1,it,is,in)a1i1atitasisanin = ( 1
9、)(i1,is,it,in)a1i1asisatitanin= D.21.9e1 1 ,ud1 . 5 1.10k1 D, 1 1 D1Dk .=D1=kD. y.kI DIsI I D1.wD1=( 1)(i1,i2,in)a1i1(kasis)anin =k( 1)(i1,i2,in)a1i1asisanin=kD, a+a a+a a+a j1jnj2j2jn j1 5 1.11D= = a j1aj2ajn aj1aj2ajn + . (dn1.6). 高校线性代数讲义前面有对学问的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物 y.D= ( 1)(i1,in)aa 1i1(jij+ajij)anin = ( 1)(i1,in)a1i n)1ajijani(i1,in+( 1)a1i1a jijanin.2 1.12e1 k1A1,u1 . 5 1.131 , 1( ), 1k ,u1 C.y.dS 1.111.12 .2.O D= 1201 132 50 015 . 36 1 234 5 0 1 A.D=1 1201 12 23100 1 0 110 2 1201 03518 = 03 518 0 110 2 = 515 003512 1201 1015 4
